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Derivatives

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AP Calculus Choice Project- Derivatives

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Questions 13

Answers

1
find the derivative of the function y=(3/(3-x))²
y'=18/(x-3)3
y'=9/(x+3)2
y'=-6/(3-x)2
y'=-18/(x-3)3
2
find the derivative of f(x)=(1+x⁴-(1/x))^5/3
f'(x)=5/3(1+x4-(1/x))1/3
f'(x)=10/9(1+x4-(1/x))2/3(4x3-(1/x2))
f'(x)=5/3(1=x4-(1/x))2/3(4x3-(1/x2))
f'(x)=5/3(1+x4-(1/x))2/3(4x3+(1/x2))
3
find the derivative of the function y=(lnx)⁶
y'=6(lnx)5(lnx)
y'=x∕(6(lnx)5)
y'=(6(lnx)5)∕x
y'=6(lnx)5
4
find the derivative of the function y=sin(x²+3x)
y'=2cosx(2x+3)
y'=sin2(x2+3x)
y'=cos(2x+3)
y'=cos(x2+3x)(2x+3)
5
find the derivative of f(x)=7^x
f'(x)=7x
f'(x)=(ln 7)(7x)
f'(x)=x(7)x-1
f'(x)=(ln 7)(x)
6
Differentiate y=5/x³
y'=15x2
y'=5/3x2
y'=5/3x2
y'=-15/x4
7
find the derivative of y=ln(sinx)
y'=cotx
y'=1/(cosx)
y'=1/(sinx)
y'=tanx
8
find the derivative of the function y=x√(1-x²)
y'=(1-2x2)/(1-x2)1/2
y'=1/2(1-x2)-1/2
y'=1/(1-x2)1/2
y'=-2x/(x)1/2
9
find the derivative of the function y=log₂(2x+1)
y'=2/[(ln2)(2x+1)]
y'=[2(ln2)]/(2x+1)
y'=(ln2)/(2x+1)
y'=2log2(2x+1)
10
what is the derivative of the function y=cos^-1x
y'=1/(1+x2)
y'=-1/(1-x2)1/2
y'=-1/(1+x2)
y'=1/(1-x2)1/2
11
find the derivative of the function y=cos√x
y'=(-sin√x)/(2√x)
y'=-1/2(sinx)2
y'=(cos√x)(2√x)
y'=(-sinx)(2√x)
12
find the derivative y= e^xsin²x
y'=2excosx
y'=exsinx(2sinx+tan2x)
y'=-2excos2x
y'= exsinx(2cosx+sinx)
13
Find the derivative of the function y=tan(lnx)
(sec2(lnx))/x
(lnx)/tanx
sec2/x
x/(sec2(lnx))